Spring-mechanism



Dec. 9, 1958 E. WILDHABER 2,853,528

SPRING-MECHANISM Filed April 26, 1954 4 Sheets-Sheet 1 INVENTOR. E. M LDHABER Dec. 9, 1958. E. WILDHABER 2,863,523

' SPRING-MECHANISM Filed April 26, 1954 4 Sheets-Sheet 2 FIG. l2

INVENTOR.

E WI LDHABER Dec. 9, 1958 E. WILDHABER 2,863,528

SPRING-MECHANISM I Filed April 26. 1954 4 Sfleets-Sheet 3 IN V EN TOR.

E- Wl LDHABER 4 Sheets-Sheet 4 Dec. 9, 1958 E. WILDHABER SPRING-MECHANISM Filed April 26. 1954 I84 III/11111110 with one winding and which will United States Patent Ofiice SPRING-MECHANISM Ernest Wildhaber, Brighton, N. Y. Application April 26, 1954, Serial No. 425,698 13 Claims. (Cl. 185-37) The present invention relates to spring mechanisms, and more particularly to a spring mechanism in which a spiral spring is employed and which is used to exert torque in accordance with a predetermined pattern different from the direct characteristic of the spring.

The torque of the conventional spiral spring varies considerably as the spring runs down. The conventional spiral spring has, therefore, to store up much more energy than is needed for operation because'its torque varies so much. In clocks, motion picture cameras, etc., which rely on regulating devices, such as pendulums, speed governors, etc., for accurate operation, the excess torque is destroyed.

One object of the invention is to provide a spring mechanism employing a spiral spring which is capable of producing torque in accordance with a predetermined pattern, where the torque is correlated to the angular deflection.

Another object of the present invention is to provide a spring mechanism capable of producing an approximately constant torque at all angular deflections used.

A further object of the invention is to provide a spring mechanism for transmitting constant torque which will improve the functioning of such devices as clocks, motion picture cameras, etc., which rely on regulating devices for accurate operation, such as pendulums, speed governors and the like.

Another object of the invention is to provide a spring mechanism which will run for a longer length of time be more accurate in operation.

Another object of the present invention is to provide a spring mechanism which for a given length of operation will be easier to wind, requiring less effort.

Another object of the invention is to provide a spiral spring of maximum load capacity and one which is stressed by a pure bending moment at the position of maximum stress, so that all portions of the spring are uniformly stressed.

Another object of the invention is to provide a spiral spring with linear, or very nearly linear, characteristics, where the transmitted torque is proportional to the angular deformation.

Another object of the invention is to provide a spiral spring with linear, or very nearly linear, characteristics so that the simplest kind of varying ratio gearing can be used with it to obtain a constant torque effect.

Another object of the invention is to provide a spring mechanism containing a spiral spring, and where the torque directly obtained from the spring is changed to a predetermined pattern through use with the spring of varying ratio gearing, and especially through use of varying ratio gearing where the two intermeshing members of the gearing move bodily, one with respect to the other as they turn.

Another object of the invention is to provide a spring mechanism incorporating varying ratio gearing in which the two toothed members of the gearing "are bodily mov- Patented Dec. 9, 1958 able one with respect to the other along the axis of one of said members.

Another object of the invention is to provide a spring mechanism in which a spiral spring is attached at one end to a face gear having teeth arranged along a spiral, and this face gear meshes with a cylindrical pinion that follows this spiral.

Other objects of the invention will appear hereinafter from the specification and from the recital of the appended claims.

In the drawings:

Figs. 1 to 4 inclusive are diagrams explanatory of the principles underlying the present invention, Figs. 1 and 2 referring to a spring with linear characteristic in a device for producing a constant torque, and Figs. 3 and 4 referring to a general spring characteristic in a device for producing a predetermined changing torque;

Fig. 5 is a fragmentary diagrammatic view illustrating an Archimedean spiral and some of its characteristics;

Fig. 6 is a fragmentary diagrammatic view of a face gear having teeth arranged along an Archimedean spiral,

' and showing a spur pinion in section in mesh with this gear, and a disc rigid with the pinion for controlling the axial position of the pinion with respect to the face gear, the sections through the pinion and disc being taken along the top of the teeth of the face gear;

Fig. 7 is a fragmentary diagrammatic view, similar to Fig. 6 but showing an improved pinion-position controlling member; 7

Fig. 8 is a section through the pinion taken perpendicular to its axis and showing, also, a fragment of the mating face gear in section;

Fig. 9 is a plan view of a spring mechanism constructed according to one embodiment of the present invention, looking at the face gear, and showing some of the parts in section;

Fig. 10 is a fragmentary view, partly in side elevation, and partly in section, of the mechanism shown in Fig. 9, the portion shown in section being taken through the pinion axis and parallel to the gear axis;

Fig. 11 is an end view taken from the right of Fig. 9 and showing the planet carrier and also a section of the winding shaft of this mechanism;

Fig. 12 is a fragmentary view showing particularly a modified form of pinion such as may be employed in a spring mechanism constructed according to this invention;

Fig. 13 is a fragmentary view showing a modification of the spring-winding and torque mechanism of Fig. 9;

Fig. 14 is a section on the line 14-14 of Fig. 13 lookingin the direction of the arrows;

Figs. 15 to 17 inclusive are diagrammatic views, showing in somewhat exaggeratedway the preferred method of determining the spring spiral before and after deflection, Fig. 15 showing the spring in partially uncoiled position, Fig. 16 showing the spring in completely coiled position, and Fig. termining the spiral;

Fig. 18 is a partial plan view, more or less diagrammatic, of a face gear such as may be employed in another embodiment of the invention;

Fig. 19 is a view, similar to Fig. 10, of this other embodiment of the invention; and

Fig. 20 is a view looking along the axis of the face gear at the spring end of the device of this embodiment. Referring first to Fig. l, 25 denotes a linear characteristic of a spring. The horizontal distance OP represents the deformation, that is, in the case of a spiral spring, the turning angle of the rotatable part to which one end of the spring is attached. It is measured from the position 0 of zero torque. The ordinate PO is a measure of the torque exerted by the spring at the deformation OP. The working range of the spring may be between the end 17 showing a detail in the steps of de- I ordinates 26 and 27; As shown in the diagram the torque exerted by this spring is in direct proportion to the deformation.

In a most important embodiment of the invention a constant spring torque is desired. This constant torque is indicated diagrammatically in Fig. 2 in terms of spring deformation. As in Fig. l, the abscissa or horizontal distance represents the deformation; the ordinate, such as PQ', represents the torque delivered, which-is here constant.

To attain this constant spring torque, I combine with a spiral spring a varying ratio'gear-ing consisting preferably, of a face gear which is attached to one end ofthe spiral spring, and of a cylindrical pinion which meshes with this face gear. The face gear has teeth arranged along a spiral; and-the pinion and face gear are constrained to move bodily along the pinion axis one with respect to the other as they turn, so that the pinion follows the spiral. In this motion-a definite mean circle of the pinion, the pitch circle of the pinion, continuously contacts the spiral in the pitch point. At the pitch point, the pinion and. gear always have the same instantaneous velocity in a direction normal to the teeth. The spiral thus describes the motion between the pinion and gear, once the pinion and the direction of the pinion axis are assumed.

The pinion is made narrow enough that it contacts only one turn or the spiral at a time. The spiral of the face gear lies in a, plane perpendicular to its axis, the pitch plane ofthe gear, and the pinion axis is parallel to this plane, It, may or may not intersect the gear axis. In the embodiment illustrated in Figs. 5 and 6 the pinion axis intersects the gear axis. In all other embodiments shown it is offset therefrom.

The pitch point in any one relative position can be considered the intersection point of the spiral convolution, which is within reach of the pinion teeth, with the projection of the pinion axis to the pitch plane of the gear.

The pitch spiral We shall now describe the determination of the spiral which lies in the pitch plane of the face gear. One form of such spiral is shown at 30 in Fig. 5.

To attain a constant torque on the pinion shaft, the force exerted on the pinion by the gear teeth should be constant. When the spring has the largest deformation and delivers the largest torque to the face gear, the mesh should be near the outside end of the spiral. At the smallest deformation. within working range, the torque shouldbe near the inside end of the spiral. In this Way, the same force will be exerted upon the pinion for both the largest and the smallest deformation of the spring, while the spring will exert a torque on the gear which varies in proportion to the distance of the pitch point from the gear axis. In other words, a constant force at the pitch point is attained when the radial distance OP' (Fig. 5) of a pitch point P from the gear; center 0 isequal to distance OP of Fig. 1, or proportional thereto. This constant force results from a gear moment proportional to OP, as given in Fig. 1'. In other words, the

spiral 30 can be described by a point P which moves on radial line O'P, the projection of the pinion axis, in direct proportion to the turning angle of the gear. This spiral has a uniform pitch along radial line O,P and is known as an Archimedean spiral.

Accordingly, when a face gear with teeth arranged in such a spiral of constant pitch is connected to a spiral sDring, with a linear characteristic in accordance with Fig. 1, it will convert the varying spring torque into a constant force exerted on the pinion and into a constant torque exerted on the pinion shaft.

The above determination is based on zero friction. This; usually issufficient since the friction forces are relatively small. If desired, however, the friction forces can also be-considered.

The determination of the pitch spiral will now be described for the general or broad case, Figs. 3 and 4, where the spring characteristic is not necessarily linear, and the torque required on the pinion shaft is not necessarily constant, but follows any predetermined pattern.

As in Fig. 1, the abscissa, or horizontal base line of Fig. 3, represents the angular deformation of the spiral spring, and the ordinate represents the torque exerted by the spring on a rotatable part to which one end of the spring is attached. GI-I is one such ordinate. JK is another. The spring characteristic 31 is here a curve.

In Fig. 4, the abscissa or horizontal base line, measures the pinion turning angle. Line 32 indicates the torque of the pinion shaft required at various turning angles of the pinion. Thus, GH, measures the pinion torque at the angular position G (Fig. 3) of the spring.

We may start from the mean positions G and G. To determine the required turning position I from a given gear turning position I, we measure the shaded area between the ordinates GH and J K. This area represents the energy transmitted from or to the spring during the turning motion between positions G and I. At zero friction, this energy is equal to the energy transmitted by the pinion shaft. Accordingly, the shaded area between the ordinates GH' and J'K is equal to the area GH K] of Fig. 3. J is determined from this requirement.

In the middle position, the instantaneous turning ratio between the pinion and gear should be in the proportion of GHzGH, provided that the torques GH and GH' are measured at the same scale. At the new turning position, the instantaneous turning ratio should be in the proportion: JKaJK.

Curve 33 (Fig. 3) expresses the instantaneous turning ratio in terms of the gear turning angle. The proportion of the ordinates :GH is equal-to the instantaneous turning ratio at I. It is equal to:

With the instantaneous turning ratio thus determined, the pitch spiral is also determined. The instantaneous turning ratio is also the proportion of the radial distance from the gear axis of the pitch point tothe constant radius of the pitch circle of the pinion. In other words, this radial distance varies exactly like the ordinates of the curve 33. It is equal to these ordinates or in a constant pro ortion thereto.

The above determination applies particularly to the case where the pinion axis 34 intersects the gear axis 29, and the pinion teeth 37 are straight. If the pinion teeth are helical, a small modification should be made in accordance with the laws of gear geometry because of the bodily relative displacement. When the pinion axis is offset, the radial distance from the projection of the gearaxis to a plane containing the pinion axis and parallel to the gear axis should be used instead of the radial distance from the gear axis directly..

After having thus determined the pitch spiral for the most important special case, where a constant torque is to be transmitted to the pinion, and in the general case, the varying ratio gearing will now be further described.

Varying ratio gearing 7 35 (Fig. 6) rigidly secured to the pinion 37 is, closer to h p 1 '0n one si Qf he proiectedpinion. axis han. o h oth rl -tcuc teslheaspi l'ononesideonly- It both sides of the disc 35 are flat or plane, the disc can touch the side wall of the spiral with edge contact only. This is an inferior kind of contact which results in rapid wear and also in extra friction.

In accordance with my invention this contact is improved in two ways, which may be used singly, or in combination. First, I provide a tapered disc as shown in Figs. 7, 9 and 10 at 36. This disc has side surfaces of revolution of unequal. profile inclination. The surface 39 adjacent the pinion teeth 37 is a plane. The surface 38 on the opposite side is a conical surface. The two opposite side surfaces of the disc 36 engage opposite sides of the spiral interdental groove 40 which follows the teeth 52 of the gear and separates adjacent turns of the spiral tooth zones of the gear. The profiles of the two sides 46, 49 of the groove 40 matchthe inclinations of the disc surfaces 38, 39, and are thus unequally inclined to the direction of the gear axis. The profile of the longitudinally concave side 49 of the groove has the larger inclination, an inclination large enough that the transverse sectional profile 38' (Fig. 7) of the mating disc is more curved than this side 49 of the groove 40, that is, than the spiral 30, so that the disc clears the spiral at the disc ends. Second, the pinion axis 54 is offset from the gear axis 55, so that the pitch spiral 43 is more nearly perpendicular to the projected pinion axis.

In a preferred embodiment with a constant pitch spiral, the pinion axis 54 is offset so that the spiral 43 is perpentdicular to the projected pinion axis at all points of inter- :section. The spiral then becomes an involute of a circle, or briefly an involute. Such involutes are shown in Figs. 7, 9 and 18. Here the pinion axis 54 is offset from the gear axis 55 an amount equal to the base radius 42 of the involute. It is tangent to the base cylinder coaxial with the face gear.

With this arrangement, the guiding disc 36 extends exactly in the direction of the spiral at the region of en gagement. It contacts the sides of the spiral groove 40 in a plane 41 tangent to the base circle 42 of the involute 43 and containing the pinion axis 54. A point of contact in plane 41 is denoted at 44 in Fig. 7. Preferably, the side surfaces of the groove 40 contain straight profiles in plane 41. The longitudinally concave side surface 49 with the inclined profile is then an involute helicoid. It has a base cylinder coaxial with the face gear and containing the base circle 42.

The pitch circle of the pinion here not only touches the pitch spiral or pitch involute 43, but has the same direction and the same tangent at all points of contact. At any such point of contact, or at the pitch point, the pinion and the gear have the same instantaneous motion in amount as well as in direction. They roll on each other without sliding. For this reason there is a minimum of tooth sliding. For this reason, also, the transmitted motion is here indepedent of the direction of the teeth. It is the same for a helical pinion as it is for a straight spur pinion.

Even in the general case, when a pitch spiral of varying pitch is required, an oifset of the pinion axis is useful to effect a direction of the spiral more nearly perpendicular to the projected pinion axis, that is, to the path of the pitch point in the pitch plane. The spiral can be kept exactly perpendicular to this path at least at a mean point. In all cases, an improvement in the contact of the guide disc 36 with the spiral groove is obtained.

In the embodiment illustrated in Figs. 7 to 11 inclusive, a spur pinion 45 having straight teeth 37 is mounted on a shaft 47 to rotate therewith and to slide axially thereon. Shaft 47 may be a spline shaft, as best seen in Fig. 8, here shown with three splines 48.

Shaft 47 is rotatably mounted in bearings 50, 51, rigid withthe stationary housing, not shown. A guide disc 36;isrigi.dly secured to the pinion 45. The pinion 45 mehswithteeth 52.0f a face gear 53. The teeth 52Jare arranged along an involute, one of the described pitch spirals. In Fig. 9, these teeth are indicated somewhat diagrammatically by stylized tooth tops, which sufficiently describe the position of the teeth. The opposite sides of the actual tooth tops vary. They tend to converge toward the outside and to meet at a point of increased radial distance, increasingly so the closer they are to the axis 55 of the face gear. The gear is rotatably mounted in two bearings 57, 58 (Fig. 10).

The face gear 53 and sliding pinion 46 constitute a vary ing ratio gearing, in which the pitch circle 45' (Fig. 8) of the pinion continuously rolls on the pitch involute 43. In this special case, the number of revolutions of the pinion per revolution of the gear is equal to the length of the pitch involute divided by the circumference of the pitch circle of the pinion. The length of the pitch involute is preferably measured from the origin, where it rises from its base circle, or where its extension rises from the base circle. This point 0 is shown in Fig. 7.

It takes a turning angle 6 of the involute to move its intersection point with tangent .1 from origin 0 to a point such as P. This angle is the turning angle it takes for the base circle to roll on tangent 41 a distance O P'. If c denotes the radius of the base circle, this turning angle amounts to:

The pinion turning angle 0 in radian measure is the product of Zr and the number of turns, that is:

This relationship applies not only to involute pitch spirals, but also to other spirals of constant pitch, for instance, to the Archimedean spiral. It expresses a kinematic relationship rather than a specific spiral, which depends also on the position of the pinion axis.

The gear may be made of steel or any other suitable material, metal or non-metal. When the production is large enough it may be pressed to shape in a die; also casting the teeth is possible. In either case a master should be made first which has teeth identical with those of the final gear except for a possible slight shrinkage, or expansion, allowance. This master is generated with a pinion-shaped cutter which describes the pinion teeth as it reciprocates. In addition to this cutting motion, the gear and cutter turn on their respective axes very slowly in the required varying proportion. After each stroke, the pinion is turned through a small angle, which may be kept constant, and the gear may be turned to a corn puted position, in accordance with the above described relative motion. Also, if desired, the varying turning motion of the gear may be controlled automatically in known manner.

After the master has been made, the working die is obtained therefrom as a counterpart, for instance, by using the master as a. die. The teeth are preferably made short enough to avoid excessive undercurrent.

In operation, as the gear and pinion rotate in mesh with each other, the pinion slides slowly on its shaft so as to follow the tooth spiral or involute. This axial motion is controlled by thetapered disc 36 through its engagement with the spiral groove 40, which follows the teeth. Thus, the varying torque of the spring 60, applied to 7 face gear, is transformed into a constant torque transmitted to the pinion 45 and its shaft 47, and to the gears driven therefrom.

The spring 60 indicated in Fig. is made from flat stock. At its inside end it is securely clamped to the hub portion 59 of gear 53 in any suitable known way. I have shown a sleeve 61 of less than a complete turn as part of the clamping means. It acts somewhat like a snap ring. The outside end of the spring is clamped to a stationary part not shown. A preferred form of spring design will be described further hereinafter.

Transmission and winding The torque is transmitted from the pinion shaft 47 through conventional gearing to the element (not shown) which is driven by the spring. In Fig. 9, the torque is shown as transmitted through planetary gearing consisting of a sun gear 62 rigidly secured to the pinion shaft 47, a planet, or a plurality of planets 63, a planet carrier 64, and a driven sun gear 65 formed integral with another gear 66 and rotatably mounted on a portion of the pinion shaft 47. Gear 66 may mesh with another pinion 667 to transmit torque. Each planet 63 contains a pinion 68 and a gear 69 rigid therewith, and is rotatably mounted at opposite ends in the planet carrier. The latter is made up of two parts 64, 64 rigidly secured to each other. Part 64 contains a circular dove-tail portion 70 by means of which the carrier is rotatably mounted in stationary parts 72. Theshaft portion 73 of the dove-tail portion 70 is mounted in a bearing 74. A winding part 75 with two arms 76 (indicated in dotted lines) is keyed to the outside end of the shaft portion 73.

Part 64 of the planet carrier contains ratchet teeth 77 on its outside face. They are engaged by a suitable pawl, not shown, held by a stationary portion, and constitute therewith a one-way clutch. Through this means the planet carrier is rotatable only in one direction. The planet carrier is normally stationary; and the spring pressure keeps it pressed against the pawl.

Looking at Fig. 9, the face gear 53 turns clockwise under the spring pressure so that the pinion 45 gradually shifts toward the center of the face gear. The pinion thereby turns counter-clockwise when looking from the left, so that the pressure exerted on the planet carrier results in a counter-clockwise torque. This torque is taken up largely by the pawl.

To wind the spring, the planet carrier is turned through the winding key arms 76 in a clockwise direction when looking from the left. The opposite Winding direction could beobtained by using a face gear and spring of opposite hand.

The winding operation leaves the tooth pressures unchanged, so that the same constant torque continues to be applied to the gear 66 and pinion 67 even in the winding operation. practically stand still, even in a clock drive, and the planets 63 roll around the sun gear 65. The turning mo tion of the planets is, however, small as compared with the turning motion of the planet carrier. Through the winding operation, the pinion 45 returns to its position near the outside end of the face gear.

A somewhat modified form of gearing is indicated in Fig. 12. Here the pinion 45" has helical teeth 37" of such hand that the resultant thrust is toward the longitudinally convex side 46 of the guide groove 40, that is, toward the left in Fig. 10. Only one side of the disc 36" then has engagement with the spiral groove of the face gear. In this way the separating force between the pinion and the gear may be reduced. The same straight splines 48 may be used here as in the previously described embodiment of the invention.

Figs. 13 and 14 illustrate a modification as regards transmission of the torque and spring winding, all other parts. remaining the, same as in, the embodiment of, Figs. 6 to 10. Here; the winding key 75! isv mounted, directly on In this operation, gear 66 and sun gear 65 when it is uniformly stressed throughout its length.

the shaft 47' of the pinion 45. Shaft 47 is mounted adjacent the center of the face gear like the shaft 47 of Fig. 10. On the opposite end it is mounted in a bearing 80. Rigidly secured to the shaft 47 is a ratchet wheel 81. This ratchet wheel is engaged by a pawl 82 which is secured by screws 89: and plate 89 to a projection 84 of a gear 83. This gear is mounted to turn on the hub of the ratchet wheel 81. The gear 83 transmits the torque to the element with which the spring mechanism is employed.

The ratchet wheel. 81 and pawl 82 constitute a one-way clutch to transmit the torque caused by the spiral spring in a direction which corresponds to a reduction of the energy stored in the spring. The clutching means leave the ratchet wheel and the pinion shaft free to turn in the opposite direction; Accordingly, the device can be wound through the pinion shaft by turning the pinion shaft by means of the key 75 in a direction opposite to the spring pressure, so that the pawl slides over the teeth of the ratchet wheel and leaves the gear 83 and the train driven by it unaffected.

The pawl 82 is here in the form of a thin fiat spring secured to a lateral projection 84 of gear 83. Any other suitable pawl may be used, however. Indeed, it does not have to be a pawl, as long as one-way clutching means results.

Instead of winding the spring device directly through the pinion shaft 47, or a shaft coaxial therewith, it could also be wound through a shaft connected with the pinion shaft througha pair of gears.

The spring Any spiral springhas the maximum possible efficiency In other words, the spring should be stressed by a pure bending moment which is transmitted throughout the length of the spring.

In one end position of a spiral spring, the spring is wound up tightly so that its adjacent coils touch each other, or nearly do so. In the other end position, the spring is more uncoiled, and its coils are more separated. One end position may be outside of the working range, and may correspond to zero stress. Ordinarily the fully coiled-up position corresponds to the maximum stress; and the more uncoiled position is the position at zero stress, the natural position. However, the positions can also be reversed.

Fig. 15 shows the more uncoiled position, while Fig. 16 shows the fully coiled up position of the spiral spring 85. For simplification, a coiled up shape is considered, where the spring extends along. the simplest spiral of constant normal separation, that is, along an involute. In order to illustrate the construction of such a spring, the thickness of the spring has to be grossly exaggerated, since it is only in this way that it is possible to show the base circle of the'involute. Ordinarily the outside of the fully coiled up spring looks like a cylindrical surface, and the base circle of the involute shrinks to what would look like a point. Its diameter is about one third of the thickness of the spring, for its circumference is equal to the spring thickness.

The conclusions reached for the involute shape of the coiled up spring also apply to other shapes, because of the very small difference therefrom in most applications.

The shape of the spring spiral will now be determined in such way that in the position of maximum stress it is stressed by a pure bending moment so that the stress is constant all along the length of the spring. If, as is usual, the coiled up position (Fig. 16) represents the position of largest stress, then we want to determine the shape of the more uncoiled spring (Fig. 15), that is, the shape of the spring spiralat zero stress, or at any other smallerstress. which corresponds to a pure bending mo-- merit. Knowing this shape, weshall be-in'a position to" at least partially fulfill the conditions which bring about the desired constant stress. I

In the diagram of Fig. 15 the adjacent coils of the spring are in contact, or near contact, with eachother. The center line 86 of the spring spiral is an involute with base circle 87. The spiral 88 of the outside surface of the spring and the spiral 90 of the inside surface of the spring are also identical involutes, as if they 'were obtained by turning involute 86 about the centerof its base circle. As known, i'nvolutes 88, 90 have a constant nor mal distance from each other. They thus correspond to a spring of constant thickness throughout its length.

The two ends of the considered spring are clamped to different parts, of which one is rotatable. Let it be assumed that at its inner end the spring is clamped at point 91, at which the spring is shown broken off. In wardly of point 91, the spring shape is controlled by the clamping means and does not concern us at present.

Let us consider now especially the involute part of the spring, namely, the part between the points 91 and 92. Straight line 91-92 is tangent to the base circle 87. The radius of curvature at any point of the involute 86. is its distance from the point of tangency with the base circle of the normal passing through the considered point. Thus at point 92, the radius of curvature is equal to the distance of point 92 from the point of tangency of line 92-91 to the base circle. In other words, the curvature center lies on the base circle.

Let R denote this radius of curvature.

When a different pure bending moment is applied to the spring, or zero moment, as compared with the maximum moment, is applied to the involute shape of the spring, the spring unbends to a degree. The curvature of the involute spiral is then altered by a constant amount This change depends in known manner on the cross section of the spring.

If the end of the spring outwardly of point 92 is straight at zero stress (Fig. 15) then at the stress transmitted through the involute (Fig. 16) it is bent to a radius R At each point of the spring the curvatures change from EFF.

The involute is thereby transformed into a different spiral 86', see Fig. 15.

The spiral It will now be shown how the spiral 86' can be determined from the involute 86. Both spirals are located in the center of the spring stock and constitute its neutral line. They have the same length. Each point of spiral 86 has a corresponding point on spiral 86'. Thus points 92 (Fig. 16) and 92' (Fig. 15) correspond to each other.

Any spiral can be described mathematically with coordinates of its points with respect to a given reference point. As reference or origin, we choose the inner ends of the spirals. On the involute it is the point 0 where the involute rises from its base circle, namely, the point of tangency of the line 91-92 (Fig. 16) with the base circle 87. As coordinates we choose the angle between the tangent at any considered point and the tangent at the origin, and the distance of the tangent at said considered point from the origin, or from the center of the base circle. Thus at point 91 of'the involute 86 the tangent is perpendicular to the line 9192 and parallel to-the tangent at the origin. The angular coordinate is there an 10 integral number of turns, namely, three turris', 6r '3 (211-) in radian' measure. Also, the distance of the tangent from the origin is three times the linear pitch of the involute 86, that is, three times the circumference of its base circle 87.

H c denotes the radius of the base circle,.the distance 7 The angular coordinate 0 of a point of spiral 86' is therefore smaller than the angular coordinate 0 of involute 86 by an amount proportional to the length of the involute to the corresponding point, and to i The length of the involute to a point with angular coordinate 0, in radian measure, is: V200 The reduction of the angular coordinate 0 is therefore And coordinate 9 is:

Instead of using radian measure, it is convenient to use number of turns T, T.

The above equation is then transformed to:

where p=21rc.

Spiral 86' can now be determined, starting from any suitable intermediate point with a number of turns T. p and R are given. The radius of curvature R of the involute at that intermediate point is:

Accordingly, the radius of curvature R of spiral 86' is at corresponding point:

The spiral can be considered composed of small portions of its curvature circles. Fig. 17 illustrates the construction through circular arcs. 94 is the center of the are for the angle 95. This center, and the radius of the are which approximates the spiral, is computed for the middle position. Beyond angle 95 new centers are required. Thus, center 96 will be good for an angle 97. The distance 94-96 is the difference of the radii of the arcs used. It is equal to the computed difference of the curvature radii at the middle of the respective angle. This consideration in terms of small portions of the,curvature circles 'of the spiral is carried onto a; further center 98 and to ;one; end of the SPlTEiLZ.ILQCOl'ltiIlUfiSJjHZ the same R, l R l. I R.

All practical combinations are solved by computing a dozen or two spirals, each with a different proportion of The computation merely expresses the above construction. It can be kept at any desired accuracy, which can be increased by. reducing the angular intervals 95, 97.

Instead of working with the spiral itself in the applications it is advantageous to work with a characteristic curve. This curve contains the points with parallel tangents on successive turns. 103 in Fig. 15 is one such point having a tangent 104 parallel to the tangent to the tangent at the origin. The characteristic curve may be plotted on a large scale together with its points of intersection 103 with the turns of the spiral. If desired, intermediate points may also be plotted on the curve. The number of turns in the coiled up position may also be plotted thereon. This curve then supplies all the required information for the given proportion it represents. If desired, tabulation can be substituted for the graph.

While the spiral 86 corresponds to the full length of the involute, starting from its origin where it rises from its base circle, allowance can readily be made for clamping at any point 91. If point 91 is fixed with reference to the turning center, the coordinates of the outer end point 92 of the spiral proper are obtained by subtracting the coordinates of point 91' from those of the outer end point 92 and adding thereto the fixed coordinates of point 91. The turning center is in the same position with respect to point 91 and to the normal 106 (Fig. 15) at that point before and after deformation in Figs. 15 and 16.

107, 107' denote the corresponding clamping points in Figs. 16 and 15, the points where clamping starts at the outside end of the spring spiral. Two properties are illustrated by these two figures, which correspond to pure bending moments, or zero stress in one case. With the conditions as assumed first, the points 107, 107' are at different distances from the center of the spirals, 107 being at the greater distance; and second the center line of the spring is inclined to the direction of the periphery at these outer clamping points. In Fig. 16, 108 is the direction of the periphery, at right angles to the radius 110 to the center of the spiral.

In one embodiment of my invention the spring is stressed by a constant pure bending moment all along its length at least near the position of maximum stress. To this end the spiral spring, which has the shape shown in Fig. 15 in its unstressed position, is clamped at its outer end in the manner shown at 107 (Fig. 16). Point 107 is placed at the required distance from the center of the spiral; and the spring is clamped in the required position inclined to the peripheral direction 108. The inclination angle is at least 30 in most cases.

The angular position of the spring at clamping point 107 is found to be more important than the radial distance. A change in the angle affects the conditions more than a'change in radius.

Computation may be supplemented by actual test. The spring may be mounted on a-pair of antifriction'cross slides so that it can only take up a pure bending moment, a pure couple, and no individual forces. The spring then will find its own position with respect to the clamping point. This position is then duplicated by the actual clamping angle. and the clamping distance. In this test the coils of the spring should be close to each other, but they should not actually touch.

Springs made and clamped in the described way have increased strength, because the whole length of the spring is equally stressed when the stress is near the maximum. Even though this clamping does not fit the other elastic positions (Fig. 15) exactly, the stress is more nearly constant all along the length of the spring also in these other positions.

Springs stressed by pure moments in all positions give turning angles in direct proportion to the moment, or also give moments in direct proportion to the turning angle. They have a linear characteristic. This is because the change in curvature l is proportional to the moment as known; and the turning angle is the product of this factor 1 'R; and the length of the spring.

Springs with linear characteristics make a spring mechanism with constant torque output, when employed with the preferred form of face gear, namely, the face gear having teeth arranged along an involute pitch line.

Springs of the character described can be made in any suitable known way. Their shape in the unstressed position has been determined above, and the coiling should be adapted to produce this shape. In some instances, the springs can be formed by casting or molding. The latter is true especially in the case of non-metallic springs such as springs made of nylon and other materials.

Spring with outer end movable toward and away from axis As has been shown in connection with Figs. 15 and 16 the outer clamped end 107, 107 should have a varying distance from the spring axis, which is at the center of the base circle 87, to attain a constant stress all along the spring and also a linear spring characteristic. One embodiment of the invention incorporating such a spring will now be described with reference to Figs. 18 to 20.

In this case the mechanism comprises a face gear 150, a cylindrical gear or pinion 151 meshing therewith, and a spiral spring 152 whose inner end is clamped to the hub of the face gear. The cylindrical pinion 151 is rotatably mounted in bearings 153, 154 in an axially fixed position. The face gear 150, however, is mounted for both rotation and bodily movement. It is bodily movable in the direction of the axis 155 of the cylindrical pinion 151. This pinion has helical teeth 156 which mesh with the teeth 157 provided on the face gear. In the instance illustrated the teeth 157 are arranged along an involute with a base circle 160. In Fig. 18 the pinion axis coincides with the tangent 161 to the base circle. Here the teeth of the face gear are shown diagrammatically.

Fig. 20 shows the spiral spring 152 in its coiled up posi tion. It is clamped at its outside end, between the stationary projection 163 and a plate 164 rigidly secured thereto as by a screw 165. The spring has a formed inner end 166 which is clamped to the hub 167 of face gear 150 by means of a circular arcuate elastic holder 170 which approaches a complete circle. Holder 170 may also be a snap ring. It presses the spring end tightly to the hub and securely clamps it thereto. if desired, the spring and may be further held by a face key. Also, any suitable known Way of clamping the spring may be used.

In the illustrated example, the coiled up position shown in Fig. 20 is the spring position of maximum stress; and care is taken that the spring is stressed by a pure bending moment. The natural tendency of the spring is to un- "13 coil and to turn the face gearin clockwise direction when looking at Fig. 20. Looking at the face gear in the opposite direction as in Fig. 18 the spring tends to turn the face gear in counter-clockwise direction.

Accordingly, the teeth 157 of the face gear are arranged in an involute of such hand that the face gear moves tr ward the cylindrical gear or pinion 151 as it turns under the spring torque. This motion is controlled through the engagement of a circular disc 172, that is secured to the pinion, with the longitudinally convex side 173 of the interdental groove 174 of the gear. The groove 174 follows the teeth 157 and extends along an involute having the same base circle 160 as the pitch involute of the teeth.

The hand of the helical teeth 156 of pinion 151 is so chosen that an inward axial thrust is exerted on the pinion teeth through the spring load, which tends to approach the pinion to the axis of the face gear, and to approach the face gear toward the pinion. Thereby the longitudinally convex side 173 of the spiral groove is pressed toward the side 176 of disc 172 to maintain constant engagement therewith. This side 176 is an internal conical surface; and side 173 of the groove 174 has an undercut straight profile 177 to match the internal conical surface. In other words, side 173 has a negative pressure angle.

The load reaction exerted on the face gear by the disc 172 has therefore an upward component as well as a component in the direction of the pinion axis. The upward component balances the downward component of the tooth load; and the other component balances the thrust exerted in the direction of the pinion axis. The resultant load reaction exerted by pinion 151 on the face gear 150 is along the pinion periphery in a direction perpendicular to the line 161 (Fig. 18). In other words, the face gear is securely held by the pinion 151, and its disc 172 in such way that only this load reaction is exerted on it.

It should be noted that the pinion 151 should be made large enough that the internal conical surface 176 of its disc 172 is curved in peripheral direction no more than the minimum lengthwise curvature of the longitudinally convex side 173 of groove 174. This minimum curvature occurs at the outside end of the spiral. In other words, the spiral surface should be more convex than the conical surface is concave, to insure the proper contact.

Because of this known direction of the load reaction it is not necessary to mount the face gear on a slide. An arbor 180 is rigidly secured to the face gear or formed integral therewith. It contains pin-shaped ends 181, 182 on which are mounted the rollers 183. The rollers engage two parallel stationary ways 184 that extend along the pinion axis, each having plane side surfaces 185 and a plane bottom surface 186.

The said load reaction is perpendicular to the sides of these ways, and is split up between the two rollers. In addition, a practically pure moment is exerted upon the face gear by the spiral spring, balancing the couple of said load reactions and of the roller reactions.

As the face gear turns on its axis 190 (Fig. 20) under the spring torque, its axis gradually moves toward the pinion to an end position 191. In this position the outer end of the spring has a shape as indicated in dotted lines 192.

The spiral spring and the clamping are determined in accordance with the principles here laid down, so that the spring exerts a pure torque not only in the position of maximum stress, but also in an intermediate position adjacent end position 191. The spring then exerts a practically pure moment throughout its working range.

As in the other embodiments described the spring is wound through the pinion shaft 193 so that the applied torque reaches the face gear through the pinion. The device may be wound from the outside through a key 75" which is here secured directly to the pinion shaft 193.

The torque caused by the spring is further transmitted from pinion or gear 151 to a small pinion 194, and thence through a one-way clutch or ratchet device 195 to a gear 196. From there it is further transmitted through gearing and shafts (not shown) to the parts where the spring torque is consumed.

The parts 194, 195, 196 and the connecting shaft are shown out of their natural positions and are indicated in dotted lines.

The spring mechanism of the present invention has application in clocks and other time pieces, in cameras for taking moving pictures, in phonographs, in machine tools for replacing counter-Weights by a device without much inertia, for spring operation of many motions, and in many other places. The spring mechanism of the present invention is easier to wind; it requires less effort than ordinary spring mechanisms. Usually less than half the energy has to be stored up in the spring for a given length of operation. Furthermore winding is more convenient because the spring torque is constant on the pinion shaft and at the winding end. No extra hard twist is needed near the end of the winding as is the case with conventional springs.

While the invention has been described in connection with several different embodiments thereof, it is capable of further modification, and this application is intended to cover any variations, uses, or adaptations of the invention following, in general, the principles of the invention and including such departures from the present disclosure as come within known or customary practice in the art to which the invention pertains, and as may be applied to the essential features hereinbefore set forth, and as fall Within the scope of the invention or the limits of the appended claims.

Having thus described my invention, what I claim is:

1. A spring-actuated mechanism for transmitting torque to a rotatable shaft in accordance with a predetermined pattern, comprising means for holding said shaft in axially fixed position, a spiral spring, a rotatable part to which one end of said spring is attached, said part having its axis at right angles to the axis of said shaft, a face gear rigid with said part and having teeth arranged along a spiral of constant pitch, a cylindrical pinion meshing with said teeth, said pinion being slidably secured to said shaft to rotate therewith, and guide means for moving said pinion bodily along said shaft as it rotates, to follow the spiral of the teeth of said gear.

2. A spring-actuated mechanism for transmitting torque to a rotatable shaft in accordance with a predetermined pattern, comprising a spiral spring, a rotatable part to which one end of said spring is attached, a face gear rigid with said part and having teeth arranged along a spiral, a cylindrical pinion meshing with said teeth, said pinion being slidably secured to said shaft to rotate therewith, the axes of said face gear and of said shaft being offset from each other in a direction so that the projection of the pinion axis to the face of said gear is more nearly perpendicular to the spiral of the teeth of said gear than a line radial of the gear axis, and guide means for moving said gear and pinion bodily, one with respect to the other, along said shaft as they rotate, so that said pinion follows the spiral of said teeth.

3. A spring-actuated mechanism for transmitting torque to a rotatable shaft in accordance with a predetermlned pattern, comprising a spiral spring, a rotatable part to which one end of said spring is attached, a face gear rigid with said part and having teeth arranged along a spiral of a plurality of convolutions and having an interdental groove separating adjacent convolutions of the teeth and following the spiral of said teeth, the longitudinally concave side of said groove having a larger profile inclination than the longitudinally convex side, a cylindrical pinion meshing with said teeth and mounted to slide axially on said shaft andto rotate therewith, and a circular disc secured to said pinion engaging said groove, to move said pinionalong said .shaft as it turns,

so that said pinion follows the spiral of said teeth, said disc having sides of unequal profile inclination in accordance with the unequal profile inclination of the groove of said gear.

4. A spring-actuated mechanism for delivering approximately constant torque to a shaft, comprising a spiral spring, a rotatable part to which one end of said spring is attached, a face gear rigid with said part and having teeth arranged along an involute in a pluralityof convolutions, said gear having an interdental groove following said involute and separating adjacent convolutions thereof, the axis of said shaft being tangent to the base cylinder of said involute, a cylindrical pinion meshing with said gear and being secured to said shaft to rotate therewith, and a circular disc secured to said pinion and engaging said groove, to move said pinion relative to said gear along said involute as said pinionrotates.

5. A spring-actuated mechanism for delivering approximately constant torque to a shaft, comprising a spiral spring, a rotatable part to which one end of said spring is attached, a face gear rigidwith said part and having teeth arranged along an involute in a plurality of convolutions, said gear having an interdental groove following said involute and separating adjacent convolutions thereof, the axis of said shaft being tangent to the base cylinder of said involute, and extendingat right angles to the axis of said part, a pinion meshing with said gear and being secured tosaid shaft to rotate therewith, and a disc rigid with said pinion and engaging said groove, said disc being disposed at a greater radial distance from the axis of said part than said pinion and having a conical surface at one side engaging one side of said groove.

6. The combination with varying ratio gearing comprising a face gear having teeth arranged on its face along an involute and in a plurality of convolutions, and a cylindrical pinion in mesh with said teeth, the axis o f Said pinion being parallel to the face of said gear and being offset from the gear axis by an amount approximately equal to the base radius of said involute, said gear having an interdentalgroove following said invol ute and separating adjacent convolutions thereof, the profile of the longitudinally concave side of said groove having a larger inclination to the axis of said gear than the profile of the longitudinally convex side, of a disc rigid with said pinion and engaging said groove, to move the gear and pinion bodily, one with respect to the other, along the pinion axis as they rotate, so that the pinion follows said involute.

7 The combination with varying ratio gearing comprising a face gear having teeth arranged on its face along a spiral of a plurality of convolutions, and having an interdental groove following said spiral and separating ad acent convolutions of said teeth, the profile of the longitudinally concave side of said groove being inclined by at least thirty degrees to the direction of the gear axis,

and a cylindrical pinion inmesh with said gear, the axis of said pinion being parallel to the face of said' gear, of

a disc rigid with said pinion and engaging said groove to constran said pinion to follow the spiral of the gear teeth as the pinion rotates.

8. A spring-actuated mechanismfor delivering torque, comprising a spiral spring, a rotatable part to which one end of said spring is attached, .a

9. A springactuated mechanism for delivering torque,

comprising aspiral'spring, a rotatable part to whicho'ne end of said spring is attached,"a' shaft for transmitting shaft for transmitting said torque varying ratio gearing disposed said torque, varying ratio gearing disposed between said part and Said. shaft, said gearing including .two rotatable toothed members bodily movable, one with respect to the other as they rotate, one of said member being rigid with saidpart, and means for winding said springthrough the other of said members, planetary gearing disposed be tween said.other member and said shaft,.said planetary gearing comprising twosun gears, a.planet, and a planet carrier in which said planet isfrotatably mounted, and oneway clutching means for maintaining one of the members of said planetary gearing normally stationary, said member being turned only in winding said spring.

.10. A spring-actuated mechanism for deliveringtorque, comprisinga spiral spring, a rotatable part to which one endof said spring is attached, said part containing gear teeth arranged in.a.spiral, a shaft mounted for rotation in an axially fixed position, a cylindrical pinion meshing with saidgearteeth and mounted in an axially fixed position on said shaft,.and means constraining said part to move bodily in the. direction of the axis of said pinion as said. pinionirotates so that said pinion follows the spiral of said gear teeth.

11.v A spring-actuated mechanism for delivering torque, comprising aspiral spring, a face gear to which one end of said spring is attached and which has teeth arranged in a spiral of a plurality of convolutions and which has an interdental groove following the spiral of said teethand separating adjacent convolutions thereof, a shaft mounted for rotation in an axially fixed position, a cylindrical pinion having helical teeth meshing with the teeth of said face gear, said pinion being mounted on said shaft inian axially fixed position, and a disc rigid with said pinion and engaging the longitudinally. convex side of ,said groove, the hand of said helical teeth being such as to drawrsaid gear towards said disc under the pressure of Saidspring, so that said gear moves bodily as it rotates.

12. Aspring-actuated mechanism for delivering torque,

comprising a spiral spring, a face gear to which one end of said spring is attached and which has teeth arranged in a spiral of aplurality of convolutions and which has an interdental groove following the spiral of said teeth and separating adjacent convolutions thereof, said groove having an undercut profile on its longitudinally convex side,..a shaft mountedfor rotation in an axiallyfixed position, a cylindrical pinion .havinghelical teeth meshing with the teeth of said gear, said pinion being mounted on said shaft in an axially fixed position, a disc rigid w th said pinion, said disc having an internally tapered side surface which engages said convex side of said groove, the hand of said helical teeth being such as to draw said gear toward said disc under pressure of Said, spring, so that said gear moves bodily as it rotates, stationary ways extending in the direction of the axis of said pinion, said gear having a plurality of cylindrical projections coaxial therewith, and rotatable parts mounted on said projections and engaging said ways. 1 13. A spring-actuated mechanismv for transmitting torque to a rotatable part, comprising a spiral spring, a pair of varying ratio gears connecting said spring and said part, one of said geas being a face gear and the other gear being a cylindrical pinionwhich meshes with said gear, and means mounting said gear for bodily movement in the direction of the axis of said pinion as the gear and pinion revolve together.

References Cited in the file of this patent UNITED STATES PATENTS 52,3 34 Smith Jan. 30, 1866 982,444 Smith Jan. 24, 1911 1,465,663 Graham Aug. 21, 1923 2,243,780 Thigpen May 27, 1941 2,501,383 Fengler Mar 21, 1950 2,570,785 Fields Oct. 9, 1951 

